Question

Use the image to answer the question.

Coordinate plane showing two right-angled triangles: Triangle ABC in Quadrant fourth and Triangle EGH in Quadrant second.

△ABC
is congruent to △GHE
. Describe a sequence of transformations from △ABC
to △GHE
that proves their congruence.

(2 points)

Math Short Answer Rubric (2 points)
This table shows the criteria for awarding points and the corresponding point values.
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.

The answer shows that the student used problem-solving skills and reasoning.

All work is shown or explained.

1
The answer is partially correct. The student made errors while solving.

The answer shows little problem-solving skills or reasoning.

Some work is shown or explained.

0 The question is not answered.


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Answer 1

One convenient sequence: rotate triangle ABC 180° about the origin.

Reason: a 180° rotation sends each point (x,y) to (−x,−y), moving points from Quadrant IV into Quadrant II. A 180° rotation is a rigid motion, so it carries △ABC exactly onto △GHE, proving congruence.

(Equivalently: reflect across the y‑axis and then reflect across the x‑axis — two reflections that produce the same result.)